Abstract
Rhythms occur at all levels of biological organization, with periods ranging from fractions of
a second to years. These rhythms have long been studied using mathematical models of an
abstract nature or based on mechanisms identified experimentally. Biological rhythms are
most abundant at the cellular level. The aim of this presentation will be to show, with the help
of selected examples, how mathematical models can be built for some of the best-known
cellular rhythms: metabolic oscillations in glycolysis, which remain the prototype of
oscillations of a biochemical nature, the 24-hour circadian clock based on a genetic regulatory
network, and the cell division cycle. Modeling the coupling between the circadian clock and
the cell cycle shows how bidirectional coupling favors the robust synchonization of these two
cellular oscillators. While the mathematical models range from the simplest (a few equations)
to the most complex (dozens of equations), the dynamic oscillatory behavior evolves each
time towards a limit cycle. The system may also evolve towards chaotic behavior, or display
multi-rhythmicity, i.e. the coexistence of two or three stable periodic solutions. In conclusion,
the presentation will address the question: "Why so many rhythms in biology?
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